What is the general solution for 2sin(x)=cos(2x) ?

The general solution for 2sin(x)=cos(2x) is x=0.37473…+2pin,x=pi-0.37473…+2pin

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2sin(x)=cos(2x)

2 sin (x) = cos (2 x)

x = 0.37473 \dots + 2 πn, x = π - 0.37473 \dots + 2 πn

Solution steps

2 sin (x) = cos (2 x)

Subtract

cos (2 x)

from both sides

2 sin (x) - cos (2 x) = 0

Rewrite using trig identities

- 1 + 2 sin (x) + 2 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{- 1 + 3}{2}, sin (x) = - \frac{1 + 3}{2}

sin (x) = \frac{- 1 + 3}{2} : x = arcsin (\frac{- 1 + 3}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 3}{2}) + 2 πn

sin (x) = - \frac{1 + 3}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 1 + 3}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 3}{2}) + 2 πn

Show solutions in decimal form

x = 0.37473 \dots + 2 πn, x = π - 0.37473 \dots + 2 πn

cos (x) = - \frac{4}{5}

2 cos^{2} (x) + 11 sin (x) = 7

cos (x) csc (x) = 2 cos (x)

cot (x) = \frac{1}{3}

2 sin (3 x - \frac{π}{3}) = - 3, 0 \leq x \leq 2 π

What is the general solution for 2sin(x)=cos(2x) ?
The general solution for 2sin(x)=cos(2x) is x=0.37473…+2pin,x=pi-0.37473…+2pin